8(x) It can be shown that for arbitrary b, 8(bx) = 5(2), and more generally, 8(b(x − x)) You can assume these results for this part of the question: i) Consider a function g(x) with one simple root at x = xo. Show that 8(g(x)) = = 8(x-xo) |b| 8(x-xo) g'(xo)|

Q: Let f(x)=9x+8‾‾‾‾‾‾√f(x)=9x+8 and g(x)=x+9g(x)=x+9 be functions from ℝR to ℝR. Find the following.…

A: We will find out the required values.

Q: Let f(x) = -3x√x + f'(x) = -8 35 -4 4 -18x³√x - ³x³√x + 24x¯4√x - NIG F X X

A:

Q: Show that f(x) = (3x - 2) / (5x - 3) , is its own inverse ?

A:

Q: 9) Given f(x)=x²-2 a) Find an expression for f¹ (f's inverse) b) Graph both f(x) and f¹(x) on the…

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Q: 13. (a) Find the inverse of the functio x) = 2x – 5 (b) Find f- (3)

A:

Q: Find f(g(x)) if f(x) = (3x+1)/x and g(x) = -2x + 1.

A: Given functions  f( x ) = ( 3x + 1 )xg( x ) = ( -2x + 1 )

Q: 4) Find f(x - 1) when f(x) - 4x2 - 4x - 7.

A: f(x) = 4x2 - 4x - 7 f(x-1) = ?

Q: Let f(x) = x + 9x and g(x) = 5-x. () Find (x) and (2).

A:

Q: f (x) = x2 - 1 / x + 4  Find the following:   5) f (2x)  6) f ( a + k)

A: Given:-   fx =x2-1x+4   now, a. f(2x) f2x=2x2-12x+4 = 4x2-12x+4 = 4x2-12x+2 = 4x22x+2-12x+2 =…

Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: 1) f(x) = 5x and g(x) = x - 3, find f(2) + g(1)

A: Please see the below picture for detailed solution.

Q: Find the derivative of the function g(x) = g'(x)= = e² 4 - 2x

A:

Q: Define f(x) = x2 + 2x-15 and g(x) = (√x+4)  (Note: x+4 all under square root) Give the value of…

A: We will find the value of (fg)(5) from the given information using the composition of functions.

Q: 3) Find domain of the following functions х+4 a) f (x) = х2+2х-8

A:

Q: Explain why both f (x) = x/ (1- x4) and g(x) = p are algebraic g(x) = -x / √(1-x4) functions.

A: f(x)=x1-x4 and g(x)=-x1-x4

Q: Let f(x)=√(x+1/x),g(x)=2/√(x-1) and h(x)=x^2+1 Describe the domains of f(x) and g(x) . Find…

A: We have to find domain

Q: Find two nontrivial functions f(x) and g(x) so f(g(x)) = (x + 6)3 f(x) =| g(x) =

A: We have to find the function

Q: Find f(f(f(1))) given 2 +3 2x – 6 if 2 5 f(f(f(1))) =

A: Given query is to find the indicated composite function.

Q: 6- Do a complete analysis to sketch the following function. F(x)=2x-x²/x²-2x+1

A:

Q: Explain how f (x) = (x − 1)2 + 3 is obtained from f (x) = x2.

A: Given f(x)=x^2, to obtain f(x)=(x-1)^2 from f(x)=x^2 we have to shift the graph to 1 unit right.

Q: What would be the piecewise function of  f(x)=(x+1)/(8-2x2)

A: Here, the equation is given by f(x)=(x+1)(8-2x2). The piecewise function of the equation has to be…

Q: 10. (a) Describe the transformations of y = x³ into the function f(x) = 8(x-1)³ -5. = (b) Describe…

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Q: Rewrite each pair of functions. (g) and g(t), as one composite function, f(g(e)). (If not possible,…

A: To find f(g(t))

Q: For each of the following functions i) f(x) = -2 x²(x² − 9), ii) g(x) = (x + 2)(x − 3)(x² − 4). a)…

A: Given function, fx=-2x2x2-9 To sketch the graph of the function, should use the some important key…

Q: Suppose that f(x) is an odd function and that f(-2)=4 Find the value of f(2)

A: Given data:     The given value of the odd function is: f(-2)=4.     The standard expression for the…

Q: f(x) = x3 -3x2 - 3x +1 x=-1 is a root of the function how would you show that?

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Q: The inflection point of the function f(x) = x³ – x² + 5x +1 is: 70 (3, 27 70 (-3,–) 27 (-3 70 (-3,…

A: Given function is fx=x3-x2+5x+1